1,162 research outputs found
Hamiltonian stationary cones with isotropic links
We show that any closed oriented immersed Hamiltonian stationary isotropic
surface with genus in is (1)
Legendrian and minimal if ; (2) either Legendrian or with exactly
Legendrian points if In general, every
compact oriented immersed isotropic submanifold such that the cone is
Hamiltonian stationary must be Legendrian and minimal if its first Betti number
is zero. Corresponding results for non-orientable links are also provided
Lagrangian Mean Curvature flow for entire Lipschitz graphs II
We prove longtime existence and estimates for solutions to a fully nonlinear
Lagrangian parabolic equation with locally initial data
satisfying either (1) for some
positive dimensional constant , (2) is weakly convex everywhere or
(3) satisfies a large supercritical Lagrangian phase condition.Comment: 17 page
Zeta Function Regularization of Photon Polarization Tensor for a Magnetized Vacuum
In this paper, we have developed a systematic technique to regularize double
summations of Landau levels and analytically evaluated the photon vacuum
polarization at an external magnetic field. The final results are described by
Lerch transcendent or its -derivation. We have found that the
tensor of vacuum polarization is split into not only longitudinal and
transverse parts but also another mixture component. We have obtained a
complete expression of the magnetized photon vacuum polarization at any
kinematic regime and any strength of magnetic field for the first time. In the
weak -fields, after canceling out a logarithmic counter term, all three
scalar functions are limited to the usual photon polarization tensor without
turning on magnetic field. In the strong -fields, the calculations under
Lowest Landau Level approximation are only valid at the region , but not correct while ,
where, an imaginary part has been missed. It reminds us, a recalculation of the
gap equation under a full consideration of all Landau Levels is necessary in
the next future.Comment: 7 pages. One severe mistake has been corrected and two references
have been update
A Precise Calculation of Delayed Coincidence Selection Efficiency and Accidental Coincidence Rate
A model is proposed to address issues on the precise background evaluation
due to the complex data structure defined by the delayed coincidence method,
which is widely used in reactor electron-antineutrino oscillation experiments.
In this model, the effects from the muon veto, uncorrelated random background,
coincident signal and background are all studied with the analytical solutions,
simplifying the estimation of the systematic uncertainties of signal efficiency
and accidental background rate determined by the unstable single rate. The
result of calculation is validated numerically with a number of simulation
studies and is also applied and validated in the recent Daya Bay
hydrogen-capture based oscillation measurement
Rigidity of Entire self-shrinking solutions to curvature flows
We show that (a) any entire graphic self-shrinking solution to the Lagrangian
mean curvature flow in with the Euclidean metric is flat; (b)
any space-like entire graphic self-shrinking solution to the Lagrangian mean
curvature flow in with the pseudo-Euclidean metric is flat if
the Hessian of the potential is bounded below quadratically; and (c) the
Hermitian counterpart of (b) for the K\"ahler Ricci flow.Comment: 10 page
Robust 3D Human Motion Reconstruction Via Dynamic Template Construction
In multi-view human body capture systems, the recovered 3D geometry or even
the acquired imagery data can be heavily corrupted due to occlusions, noise,
limited field of- view, etc. Direct estimation of 3D pose, body shape or motion
on these low-quality data has been traditionally challenging.In this paper, we
present a graph-based non-rigid shape registration framework that can
simultaneously recover 3D human body geometry and estimate pose/motion at high
fidelity.Our approach first generates a global full-body template by
registering all poses in the acquired motion sequence.We then construct a
deformable graph by utilizing the rigid components in the global template. We
directly warp the global template graph back to each motion frame in order to
fill in missing geometry. Specifically, we combine local rigidity and temporal
coherence constraints to maintain geometry and motion consistencies.
Comprehensive experiments on various scenes show that our method is accurate
and robust even in the presence of drastic motions.Comment: 3DV 2017 pape
3D Face Reconstruction Using Color Photometric Stereo with Uncalibrated Near Point Lights
We present a new color photometric stereo (CPS) method that recovers high
quality, detailed 3D face geometry in a single shot. Our system uses three
uncalibrated near point lights of different colors and a single camera. For
robust self-calibration of the light sources, we use 3D morphable model (3DMM)
and semantic segmentation of facial parts. We address the spectral ambiguity
problem by incorporating albedo consensus, albedo similarity, and proxy prior
into a unified framework. We avoid the need for spatial constancy of albedo;
instead, we use a new measure for albedo similarity that is based on the albedo
norm profile. Experiments show that our new approach produces state-of-the-art
results from single image with high-fidelity geometry that includes details
such as wrinkles
4D Human Body Correspondences from Panoramic Depth Maps
The availability of affordable 3D full body reconstruction systems has given
rise to free-viewpoint video (FVV) of human shapes. Most existing solutions
produce temporally uncorrelated point clouds or meshes with unknown
point/vertex correspondences. Individually compressing each frame is
ineffective and still yields to ultra-large data sizes. We present an
end-to-end deep learning scheme to establish dense shape correspondences and
subsequently compress the data. Our approach uses sparse set of "panoramic"
depth maps or PDMs, each emulating an inward-viewing concentric mosaics. We
then develop a learning-based technique to learn pixel-wise feature descriptors
on PDMs. The results are fed into an autoencoder-based network for compression.
Comprehensive experiments demonstrate our solution is robust and effective on
both public and our newly captured datasets.Comment: 10 pages, 12 figures, CVPR 2018 pape
Resolving Scale Ambiguity Via XSlit Aspect Ratio Analysis
In perspective cameras, images of a frontal-parallel 3D object preserve its
aspect ratio invariant to its depth. Such an invariance is useful in
photography but is unique to perspective projection. In this paper, we show
that alternative non-perspective cameras such as the crossed-slit or XSlit
cameras exhibit a different depth-dependent aspect ratio (DDAR) property that
can be used to 3D recovery. We first conduct a comprehensive analysis to
characterize DDAR, infer object depth from its AR, and model recoverable depth
range, sensitivity, and error. We show that repeated shape patterns in real
Manhattan World scenes can be used for 3D reconstruction using a single XSlit
image. We also extend our analysis to model slopes of lines. Specifically,
parallel 3D lines exhibit depth-dependent slopes (DDS) on their images which
can also be used to infer their depths. We validate our analyses using real
XSlit cameras, XSlit panoramas, and catadioptric mirrors. Experiments show that
DDAR and DDS provide important depth cues and enable effective single-image
scene reconstruction
Personalized Saliency and its Prediction
Nearly all existing visual saliency models by far have focused on predicting
a universal saliency map across all observers. Yet psychology studies suggest
that visual attention of different observers can vary significantly under
specific circumstances, especially a scene is composed of multiple salient
objects. To study such heterogenous visual attention pattern across observers,
we first construct a personalized saliency dataset and explore correlations
between visual attention, personal preferences, and image contents.
Specifically, we propose to decompose a personalized saliency map (referred to
as PSM) into a universal saliency map (referred to as USM) predictable by
existing saliency detection models and a new discrepancy map across users that
characterizes personalized saliency. We then present two solutions towards
predicting such discrepancy maps, i.e., a multi-task convolutional neural
network (CNN) framework and an extended CNN with Person-specific Information
Encoded Filters (CNN-PIEF). Extensive experimental results demonstrate the
effectiveness of our models for PSM prediction as well their generalization
capability for unseen observers.Comment: 15 pages, 10 figures, journa
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